Intersection of Sets

Pronunciation: /ˌɪn tərˈsɛk ʃən/ Explain

Figure 1: Intersection. Click on the image to see a representation of A ∩ B.

An intersection of two or more sets is a set containing the members that are in all of the sets. This is spoken, "Set C is the intersection of sets A and B." This is written, C = A ∩ B.

Properties of Intersection of Sets

PropertyMath StatementDescription
CommutativeA ∩ B = B ∩ AThe intersection of sets is commutative
Associative(D ∩ E) ∩ F = D ∩ (E ∩ F)The intersection of sets is associative
Distributive(D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F)
(D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)
The intersection and union of sets are distributive
Table 1: Properties of the intersection of two sets.


  1. intersection. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018.
  2. Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior. 3rd edition. pg 63. Princeton University Press. 1953. Last Accessed 8/6/2018. Buy the book
  3. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 8/6/2018. Buy the book
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 4. Thomson, Brooks/Cole. 2005. Buy the book

More Information

  • McAdams, David E.. Sets. Life is a Story Problem LLC. 3/12/2009.

Cite this article as:

McAdams, David E. Intersection of Sets. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
7/30/2018: Initial version. (McAdams, David E.)

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